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Find the indicated limit.$$\lim _{h \rightarrow 0} \frac{\sqrt{3+h}-\sqrt{3}}{h}$$

$\frac{\sqrt{3}}{6}$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

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Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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in this problem, we have to find the integrated limit off the given function that is limit limit Off edge approaches to zero scare route off three plus edge minus scare route off three A bon edge If we try to substitute edges ical to zero In the given function we have zero upon zero, which is an intermediate form. So we can I We cannot apply the limit directly. Now we will redefine the function using Al Jabri techniques. So for this function, we will use the rationalization method to redefine the function. Therefore, limit at approaches to zero scare route off three place edge minus K. Rudolph three divided by edge Multiply by Let us take the congregate off the numerator which is scared off three bliss edge plus super rude or three divided by So okay Wrote off three plus edge less scare Rudolph three Here we have multiplied and divided by the kinds of great off the numerator off the given function. Now a numerator, the product will be limit eight days, two of zero on numerical. We have an algebraic identity that is a minus bi multiply by a plus B which is equal to scare route off. Three plus edge. All square minus scare. Route off Pre. Also care to add it by edge in tow. Scared off. Three plus edge less scared off. Three. No, we have limit age approaches to zero Here. Scare and route will begin. So so on the monitor. We have three plus EJ minus three upon edge into scare route off creep plus edge plus K route off three. Here loss and ministry will be canceled. So we have limit at approaches to zero into It's divided by Ed into scared off three Bless edge plus K route off three. Now we can cancel. It's from new militant denominator. So we have limit at approaches to zero. Run up on numerator. We have one Suki route off three plus edge less scared. Rudolph three. Now we can apply. The limit is at approaches to zero. They're gives went up on scared off three plus zero, which is three less plus K route off. Three. From here we have went upon to scare old all three again weekend simply by further to eliminate the scared from the Terminator from the denominator. Therefore, again, we will use the rationalization method So for that we have to multiply and divide by Suki Route off three. So we have on the military. We have scared. All three divided by two times. Sochi wrote off three multiple hours to get root off threes. Three. So finally we have scare rude or three upon six, which is the required limit, which we have to find for the given function.

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